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# Memo

To: Docket EPA-HQ-OAR-20 10-0799

From: Joseph McDonald, U.S. EPA-OTAQ-ASD

CC: Ed Nam, U.S. EPA-OTAQ-ASD

Date: Tuesday, November 29, 2011

Re: Initial BatPaC Variation Study

The attached document contains a cost sensitivity analysis conducted by Argonne National Laboratory using the BatPaC model. The analysis varied cost and design input variables and estimated a confidence interval for the cost of various Li-ion cathode types and for different vehicle applications.An Initial BatPaC Variation Study Kevin G. Gallagher and Paul A. Nelson September 13, 2011 Summary
The following ranges are suggested as an initial approximation to account for variation that will occur in the cost inputs and possible design limitations in BatPaC

. The larger uncertainty for LMO in PHEV and EV batteries is due to an interaction with the electrode thickness limitation. These values do not account for any uncertainty that results from advanced Li

- ion chemistries successfully entering the ma rket place. If one considers the likely entry of less expensive and more energy dense materials , and the potential for significant improvements in manufacturing processes, the uncertainty towards lower costs will certainly increase. If a simpler approach is desired for EVs and PHEVs , using +/

- 20 % for every EV and PHEV battery modeled is a reasonable alterna tive that considers some probability of advanced technologies entering the market in the 2020 timeframe

. Future versions of BatPaC will include error estimation within the model.
Summary Table 1. Suggested confidence bounds as a percentage of the calculated point estimate for a graphite based Li

- ion battery using the default inputs in BatPaC.

Discussion
The general approach in this variation study is to produce a distribution of cost inputs and analyze a range of battery designs to capture the spread in calculated battery price if the default cost inputs or design parameters are in error. The eight largest cost contributions comp ri sing the battery price to the OEM, shown in Table 1, were evaluated to determine the range of possible values and the likely form of the distribution, normal or log

- normal. For normal distributions, the standard deviation was approximated as 1⁄4 of the range of values. The parameters for log

- normal distributions were hand

- fit to set the minimum and maximum at the outer range of the 95 % confidence interval. Equations 1 and 2 were used to create the distribution for each cost input
, C ij , from independent sets of 3000 normally distributed random numbers
, r ij . Here, C i is the mean and σ i is the standard deviation for the normal distribution of cost input i . Additionally, μ i is the location parameter and α i is the scale parameter for the log

- normal distribution. Each collection of cost inputs was used to produce an end battery price to the OEM. The battery designs used in this study are detailed in Table 2.

normal (1)( ) log

- normal ( 2 )

Table 1. Cost input ranges and distributions used in variation study

Table 2. Battery designs considered in variation study

The variation in calculated price solely due to cost input estimates results in a near

- normal distribution of values . The results may be adequately summarized by the calculated mean and standard deviation. O nly the cases of the default design limitations are shown in Table 3 (100 micron limit, 1 cell in cell group). A value of +/

- 10 % would adequately capture the 95% confidence interval of the calculated price distributions for all battery chemistries and ba ttery types. Table 3. Distribution in calculated price from cost input variationQuantifying the error in calculated price due to the relative success or failure of certain desig n

criteria is more difficult . We have chosen to vary the electrode thickness limitation for the PHEV and EV calculations. In addition, t he EV battery was also calculated in a 2P

- 96S configuration (2 cells in parallel) to capture the possibility of smaller capacity cells while maintaining the 100 micron thickness limit

. No design c hanges were analyzed for the HEVs. Treating each of the battery design occurrences as equally probable , the calculated population of each of the chemistr ies becomes a skewed distribution. Capturing the skewed and sometime bi

- modal distribution in a simple statistical fashion is not straightforward

. We suggest the use of a distribution parameter, ε , to establish the outer limits of a 95 % confidence interval from the point estimate, P o , created from the default values . This parameter is used in an empirical fashion in Equation 3 and 4 . The factor of 1.05 is used to capture the increase in the mean of the population as compared to a spot estimate using the default inputs. The distribution parameters used in this study a re twice the value of the standard deviation divided by the mean. ( ) ( 3 ) ( ) (4 )
The NMC441 and NCA cathodes for PHEV and EV data sets may be captured using a distribution parameter of 0.15. The LMO cathode requires distribution parameter of 0.28. The larger variation of the LMO cathode results from interaction with the limiting electr ode thickness. A similar behavior is expected for LFP in energy batteries as this cathode also has a low volumetric capacity. The NMC441 and NCA cathodes have a significantly higher volumetric capacity and thus are less se nsitive to this limitation. Figures 1

- 3 present the variation of the PHEV and EV trials with the suggested confidence bounds highlighted by red lines.Figure 1. PHEV25 price distributions for NMC441 / Gr batteries. Red lines denote suggested

upper and lower bounds for confidence in terval. Black line represents price calculated from default values.Figure 2. PHEV25 price distributions for LMO / Gr batteries. Red lines denote suggested upper

and lower bounds for confidence interval. Black line represents price calculated from defau lt values.Figure 3. EV100 distributions for LMO / Gr and NMC441 / Gr batteries. Red lines denote

suggested upper and lower bounds for confidence interval. Black line represents price calculated from default values.